A181447 Numbers k such that 3 is the largest prime factor of k^2 - 1.

2, 5, 7, 17

Offset: 1

Author

Artur Jasinski, Oct 21 2010

Keywords

• nonn
• fini
• full

Comments

Sequence is finite and complete, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(2) = 17; primepi(3) = 2.

Crossrefs

Cf. A175607, A181448-A181470, A181568.

Programs

Magma

[ n: n in [2..20] | m eq 3 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 17 2011

Mathematica

Select[Range[20], FactorInteger[#^2-1][[-1, 1]]==3&]

PARI

is(n)=n=n^2-1;my(o=valuation(n,3)); o && n>>valuation(n/3^o,2)==1 \\ Charles R Greathouse IV, Jul 01 2013